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Field-induced antiferroquadrupolar order in the heavy fermion superconductor PrOs4Sb12
ARTICLE IN PRESS
Physica B 378–380 (2006) 189–191 www.elsevier.com/locate/physb
Field-induced antiferroquadrupolar order in the heavy fermion superconductor PrOs4Sb12 Koji Kanekoa,, Naoto Metokia,b, Tatsuma D. Matsudaa, Keitaro Kuwaharac, Masahumi Kohgic, Ryousuke Shiinac, Jean-Michel Mignotd, Arsen Gukasovd, Nicholas Bernhoefte a
ASRC, Japan Atomic Energy Research Institute, Ibaraki 319-1195, Japan b Department of Physics, Tohoku University, Sendai 980-8578, Japan c Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan d Laboratoire Le´on Brillouin, CEA/Saclay, 91191 Gif sur Yvette, France e DRFMC-CEA, 38054 Grenoble, France
Abstract Neutron diffraction experiments under magnetic fields were carried out on the heavy fermion superconductor PrOs4Sb12 in order to reveal the origin of the field-induced ordered phase (FIOP) for Hk½1 1 0. An application of magnetic field induces the weak superlattice peaks with the ordering vector q ¼ ð1 0 0Þ in FIOP, which is the same as for Hk½0 0 1. The observed superlattice reflections for Hk½1 1 0 result from the antiferromagnetic component of J x þ J y ; the induced tiny antiferromagnetic moments orient parallel to the applied field. This result cannot be explained by magnetic interactions and strongly evidences the underlying AFQ order with Oxy as a primary order parameter. These facts clarify the dominant role of Oxy -type antiferroquadrupolar interaction in PrOs4Sb12. r 2006 Elsevier B.V. All rights reserved. PACS: 71.10.Hf; 71.27.þa; 75.30.Mb Keywords: PrOs4Sb12; Heavy fermion superconductivity; Antiferroquadrupolar order
The first Pr-based heavy fermion superconductor PrOs4Sb12 attracts considerable interest because of its unusual superconducting properties such as the double transition in the specific heat [1]. The non-magnetic G1 ground state, the field-induced antiferroquadrupolar (AFQ) order phase for Hk½0 0 1 and the neutron inelastic scattering intensity indicate the dominant role of AFQ interaction in PrOs4Sb12 [2–6]. The field-induced ordered phase (FIOP) exists for Hk½1 1 0 and ½1 1 1 as well [7]. In case for ½1 1 0, the mean field calculation suggests that the Oxy symmetry elements would be the primary order parameter but the energy difference for another one is very small [8]. Besides, the magnetization measurements reports the additional phase boundary in the FIOP for Corresponding author. Tel.: +81 29 282 6830; fax: +81 29 282 5939.
E-mail address: [email protected] (K. Kaneko). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.01.349
Hk½1 1 0 [7]. In order to clarify the origin of FIOP for Hk½1 1 0, neutron diffraction experiments were carried out. Neutron diffraction experiments for the single crystalline PrOs4Sb12 were carried out on the cold neutron triple-axis spectrometer LTAS installed at the research reactor JRR-3 of Japan Atomic Energy Research Institute (JAERI), Tokai, Japan. For the investigation of FIOP, liquid He free 10 T superconducting magnet and 3He–4He dilution refrigerator, both developed by JAERI, were used. The scattering plane was set to ðh h¯ lÞ which is perpendicular to the vertical field applied parallel to the ½1 1 0 direction. A large single crystal sample with mass of 6 g has been grown by the antimony-self-flux method. The detail of the sample preparation technique has been published elsewhere. Single crystal X-ray diffraction, susceptibility, electrical resistivity measurements for the small fraction of sample confirmed the high quality of the present sample.
ARTICLE IN PRESS K. Kaneko et al. / Physica B 378–380 (2006) 189–191
190
Intensity (103 cnt / 300 s)
1.6
(a)
PrOs4Sb12 001 0.27 K H || [1 1 0] 0 T 8 T
1.2
0.8 24
25
26
27
2 (deg.)
2.0
(b)
PrOs4Sb12 Intensity (103 cnts / 1200 Sec)
Fig. 2. Schematic view of determined magnetic structure of PrOs4Sb12 in FIOP for Hk½1 1 0.
2 -2 1 H || [1 1 0] 3 T 1.5
8 T
1.0
0.5
1.0 T(K)
Fig. 1. (a) Magnetic field dependence of neutron diffraction profile of 0 0 1 reflection at 0:27 K. The open and closed circles were taken at 0 and 8 T, respectively, applied parallel to the ½1 1 0 direction. (b) Temperature dependence of 2 2¯ 1 peak intensity measured under applied field of 3 TðÞ and 8 TðÞ.
Fig. 1(a) shows the 0 0 1 neutron diffraction profile measured at 0:27 K. The appearance of a weak but clear superlattice reflection was observed under 8 T while no trace was found at 0 T. The fieldinduced superlattice peaks were observed at the same positions as Hk½0 0 1, namely, the propagation vector is q ¼ ð1 0 0Þ. Temperature dependence of the 2 2¯ 1 superlattice peak intensity was measured under 3 and 8 T as shown in Fig. 1(b). With increasing temperature at 8 T, the 2 2¯ 1 peak becomes weaker and disappears around 0:8 K. On the other hand, no superlattice peak intensity was observed at 3 T in the whole temperature range. The phase boundary for the superlattice reflection is in good agreement with the
reported H–T phase diagram determined by the magnetization measurements [7]. In order to determine the magnetic structure in FIOP for Hk½1 1 0, the integrated intensity of superlattice peaks in the ðh h¯ lÞ scattering plane has been measured. The one important factor affecting the magnetic reflection intensity is the so-called ‘angle factor’; the magnetic scattering intensity depends on the angle between the magnetic moment and scattering vector. The intensity analysis revealed that the angle factor for the reflections in the present scattering plane is almost isotropic within the experimental accuracy. In other words, the induced antiferromagnetic moment orients parallel to the applied fields. In addition, the relatively large ferromagnetic moment is also induced parallel to the field. The sum of these two components results in the ferromagnetic structure where the magnetic moment at the corner of the unit cell is larger than that at the center, or vice versa. The determined structure of FIOP for Hk½1 1 0 is shown in Fig. 2. The induced antiferromagnetic component J x þ J y , parallel to the applied field, cannot be explained by magnetic interactions which favors the magnetic moment perpendicular to the field. This result directly evidences the underlying AFQ order in FIOP for Hk½1 1 0 with Oxy symmetry of the primary order parameter [8]. In case for Hk½0 0 1, the antiferromagnetic component of J y which couples to the quadrupole Oyz is induced in FIOP [3]. In this case, the comparison between experimental results and mean-field calculation clarifies the primary order parameter to be Oyz [4]. These facts strongly indicate the dominant role of Oxy -type quadrupolar interaction in PrOs4Sb12. We are grateful to H. Sugawara for helpful discussion on the sample preparation.
ARTICLE IN PRESS K. Kaneko et al. / Physica B 378–380 (2006) 189–191
References [1] M.B. Maple, et al., J. Phys. Soc. Japan 71 (Suppl. 23) (2002). [2] Y. Aoki, et al., J. Phys. Soc. Japan 71 (2002) 2098. [3] M. Kohgi, et al., J. Phys. Soc. Japan 72 (2003) 1002.
[4] [5] [6] [7] [8]
R. Shiina, Y. Aoki, J. Phys. Soc. Japan 73 (2004) 541. K. Kuwahara, et al., J. Phys. Soc. Japan 73 (2004) 1438. K. Kuwahara, et al., Phys. Rev. Lett. 95 (2005) 107003. T. Tayama, et al., J. Phys. Soc. Japan 72 (2003) 1516. R. Shiina, J. Phys. Soc. Japan 73 (2004) 2257.
191
Physica B 378–380 (2006) 189–191 www.elsevier.com/locate/physb
Field-induced antiferroquadrupolar order in the heavy fermion superconductor PrOs4Sb12 Koji Kanekoa,, Naoto Metokia,b, Tatsuma D. Matsudaa, Keitaro Kuwaharac, Masahumi Kohgic, Ryousuke Shiinac, Jean-Michel Mignotd, Arsen Gukasovd, Nicholas Bernhoefte a
ASRC, Japan Atomic Energy Research Institute, Ibaraki 319-1195, Japan b Department of Physics, Tohoku University, Sendai 980-8578, Japan c Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan d Laboratoire Le´on Brillouin, CEA/Saclay, 91191 Gif sur Yvette, France e DRFMC-CEA, 38054 Grenoble, France
Abstract Neutron diffraction experiments under magnetic fields were carried out on the heavy fermion superconductor PrOs4Sb12 in order to reveal the origin of the field-induced ordered phase (FIOP) for Hk½1 1 0. An application of magnetic field induces the weak superlattice peaks with the ordering vector q ¼ ð1 0 0Þ in FIOP, which is the same as for Hk½0 0 1. The observed superlattice reflections for Hk½1 1 0 result from the antiferromagnetic component of J x þ J y ; the induced tiny antiferromagnetic moments orient parallel to the applied field. This result cannot be explained by magnetic interactions and strongly evidences the underlying AFQ order with Oxy as a primary order parameter. These facts clarify the dominant role of Oxy -type antiferroquadrupolar interaction in PrOs4Sb12. r 2006 Elsevier B.V. All rights reserved. PACS: 71.10.Hf; 71.27.þa; 75.30.Mb Keywords: PrOs4Sb12; Heavy fermion superconductivity; Antiferroquadrupolar order
The first Pr-based heavy fermion superconductor PrOs4Sb12 attracts considerable interest because of its unusual superconducting properties such as the double transition in the specific heat [1]. The non-magnetic G1 ground state, the field-induced antiferroquadrupolar (AFQ) order phase for Hk½0 0 1 and the neutron inelastic scattering intensity indicate the dominant role of AFQ interaction in PrOs4Sb12 [2–6]. The field-induced ordered phase (FIOP) exists for Hk½1 1 0 and ½1 1 1 as well [7]. In case for ½1 1 0, the mean field calculation suggests that the Oxy symmetry elements would be the primary order parameter but the energy difference for another one is very small [8]. Besides, the magnetization measurements reports the additional phase boundary in the FIOP for Corresponding author. Tel.: +81 29 282 6830; fax: +81 29 282 5939.
E-mail address: [email protected] (K. Kaneko). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.01.349
Hk½1 1 0 [7]. In order to clarify the origin of FIOP for Hk½1 1 0, neutron diffraction experiments were carried out. Neutron diffraction experiments for the single crystalline PrOs4Sb12 were carried out on the cold neutron triple-axis spectrometer LTAS installed at the research reactor JRR-3 of Japan Atomic Energy Research Institute (JAERI), Tokai, Japan. For the investigation of FIOP, liquid He free 10 T superconducting magnet and 3He–4He dilution refrigerator, both developed by JAERI, were used. The scattering plane was set to ðh h¯ lÞ which is perpendicular to the vertical field applied parallel to the ½1 1 0 direction. A large single crystal sample with mass of 6 g has been grown by the antimony-self-flux method. The detail of the sample preparation technique has been published elsewhere. Single crystal X-ray diffraction, susceptibility, electrical resistivity measurements for the small fraction of sample confirmed the high quality of the present sample.
ARTICLE IN PRESS K. Kaneko et al. / Physica B 378–380 (2006) 189–191
190
Intensity (103 cnt / 300 s)
1.6
(a)
PrOs4Sb12 001 0.27 K H || [1 1 0] 0 T 8 T
1.2
0.8 24
25
26
27
2 (deg.)
2.0
(b)
PrOs4Sb12 Intensity (103 cnts / 1200 Sec)
Fig. 2. Schematic view of determined magnetic structure of PrOs4Sb12 in FIOP for Hk½1 1 0.
2 -2 1 H || [1 1 0] 3 T 1.5
8 T
1.0
0.5
1.0 T(K)
Fig. 1. (a) Magnetic field dependence of neutron diffraction profile of 0 0 1 reflection at 0:27 K. The open and closed circles were taken at 0 and 8 T, respectively, applied parallel to the ½1 1 0 direction. (b) Temperature dependence of 2 2¯ 1 peak intensity measured under applied field of 3 TðÞ and 8 TðÞ.
Fig. 1(a) shows the 0 0 1 neutron diffraction profile measured at 0:27 K. The appearance of a weak but clear superlattice reflection was observed under 8 T while no trace was found at 0 T. The fieldinduced superlattice peaks were observed at the same positions as Hk½0 0 1, namely, the propagation vector is q ¼ ð1 0 0Þ. Temperature dependence of the 2 2¯ 1 superlattice peak intensity was measured under 3 and 8 T as shown in Fig. 1(b). With increasing temperature at 8 T, the 2 2¯ 1 peak becomes weaker and disappears around 0:8 K. On the other hand, no superlattice peak intensity was observed at 3 T in the whole temperature range. The phase boundary for the superlattice reflection is in good agreement with the
reported H–T phase diagram determined by the magnetization measurements [7]. In order to determine the magnetic structure in FIOP for Hk½1 1 0, the integrated intensity of superlattice peaks in the ðh h¯ lÞ scattering plane has been measured. The one important factor affecting the magnetic reflection intensity is the so-called ‘angle factor’; the magnetic scattering intensity depends on the angle between the magnetic moment and scattering vector. The intensity analysis revealed that the angle factor for the reflections in the present scattering plane is almost isotropic within the experimental accuracy. In other words, the induced antiferromagnetic moment orients parallel to the applied fields. In addition, the relatively large ferromagnetic moment is also induced parallel to the field. The sum of these two components results in the ferromagnetic structure where the magnetic moment at the corner of the unit cell is larger than that at the center, or vice versa. The determined structure of FIOP for Hk½1 1 0 is shown in Fig. 2. The induced antiferromagnetic component J x þ J y , parallel to the applied field, cannot be explained by magnetic interactions which favors the magnetic moment perpendicular to the field. This result directly evidences the underlying AFQ order in FIOP for Hk½1 1 0 with Oxy symmetry of the primary order parameter [8]. In case for Hk½0 0 1, the antiferromagnetic component of J y which couples to the quadrupole Oyz is induced in FIOP [3]. In this case, the comparison between experimental results and mean-field calculation clarifies the primary order parameter to be Oyz [4]. These facts strongly indicate the dominant role of Oxy -type quadrupolar interaction in PrOs4Sb12. We are grateful to H. Sugawara for helpful discussion on the sample preparation.
ARTICLE IN PRESS K. Kaneko et al. / Physica B 378–380 (2006) 189–191
References [1] M.B. Maple, et al., J. Phys. Soc. Japan 71 (Suppl. 23) (2002). [2] Y. Aoki, et al., J. Phys. Soc. Japan 71 (2002) 2098. [3] M. Kohgi, et al., J. Phys. Soc. Japan 72 (2003) 1002.
[4] [5] [6] [7] [8]
R. Shiina, Y. Aoki, J. Phys. Soc. Japan 73 (2004) 541. K. Kuwahara, et al., J. Phys. Soc. Japan 73 (2004) 1438. K. Kuwahara, et al., Phys. Rev. Lett. 95 (2005) 107003. T. Tayama, et al., J. Phys. Soc. Japan 72 (2003) 1516. R. Shiina, J. Phys. Soc. Japan 73 (2004) 2257.
191